Question

George decides to walk from his home to Tina's house down the street. On the way,
he stops at the gas station to get some snacks. He begins at (2,3), ends at (9,17), and
stops at the gas station at (x,y). If the part to part ratio is 3:4, what is the coordinates
of the gas station? (Type out as a coordinate)

Answer 1

Answer:

The coordinates of the gas station are (5, 9)

Step-by-step explanation:

As given,

George begins at (2,3), ends at (9,17), and  stops at the gas station at (x,y). If the part to part ratio is 3:4

 A                   P                     B

(2, 3)             (x, y)                (9, 17)

           3         :             4

we use the Interval Division formula :

If P(x,y) lies on the interval A(x1,y1), B(x2,y2) such that AP:PB=a:b, with a and b positive, then

x= $\frac{bx1 + ax2}{a + b}$

y=$\frac{by1 + ay2}{a + b}$

Here , (x1, y1) = (2, 3)

          (x2, y2) = (9, 17)

           a : b = 3 : 4

⇒ x= $\frac{bx1 + ax2}{a + b}$ = $\frac{4(2) + 3(9)}{3 + 4} = \frac{8 + 27}{7} = \frac{35}{7} = 5$

   y=$\frac{by1 + ay2}{a + b}$ = $\frac{4(3) + 3(17)}{3 + 4} = \frac{12 + 51}{7} = \frac{63}{7} = 9$

∴ The coordinates of the gas station are (5, 9)